Yang-Mills Theory Explained: SU(N) Symmetry & Gauge Theory

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SUMMARY

Yang-Mills Theory is a fundamental gauge theory based on SU(N) symmetry, applicable to specific cases such as Electroweak theory and Quantum Chromodynamics (QCD). It requires the introduction of gauge fields to maintain gauge invariance, and the gauge group must be non-abelian to differentiate it from simpler theories like Quantum Electrodynamics (QED). While SU(N) is a common choice, other groups such as SO(N) and Sp(N) can also be utilized in Yang-Mills formulations.

PREREQUISITES
  • Understanding of gauge theory principles
  • Familiarity with SU(N) symmetry and its implications
  • Knowledge of non-abelian groups in mathematics
  • Basic concepts of Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD)
NEXT STEPS
  • Research the mathematical foundations of gauge theory
  • Explore the applications of Yang-Mills Theory in Electroweak interactions
  • Study the role of non-abelian gauge groups in particle physics
  • Learn about the differences between Yang-Mills Theory and Quantum Electrodynamics
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The discussion is beneficial for theoretical physicists, graduate students in physics, and anyone interested in advanced concepts of gauge theories and their applications in particle physics.

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What exactly is a Yang-Mills Theory? Is it a general theory, based on SU(N) symmetry, which can then be applied for particular cases (ElectroWeak, Chromodynamics) ? Is it like a general mathematical model of gauge theory ?
 
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Qubix said:
What exactly is a Yang-Mills Theory? Is it a general theory, based on SU(N) symmetry, which can then be applied for particular cases (ElectroWeak, Chromodynamics) ? Is it like a general mathematical model of gauge theory ?

Yes its a gauge theory:

http://en.wikipedia.org/wiki/Yang-Mills_theory
 
Not necessarily SU(N). It can also be like SO(N), Sp(N), etc. The idea is we need to introduce gauge fields to keep the theory gauge invariant.
 
The gauge group of the field theory needs to be nonabelian, else it would just be quantum electrodynamics.
 

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